Regularity of dynamical Green’s functions
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- by Jeffrey Diller and Vincent Guedj PDF
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Abstract:
For meromorphic maps of complex manifolds, ergodic theory and pluripotential theory are closely related. In nice enough situations, dynamically defined Green’s functions give rise to invariant currents which intersect to yield measures of maximal entropy. ‘Nice enough’ is often a condition on the regularity of the Green’s function. In this paper we look at a variety of regularity properties that have been considered for dynamical Green’s functions. We simplify and extend some known results and prove several others which are new. We also give some examples indicating the limits of what one can hope to achieve in complex dynamics by relying solely on the regularity of a dynamical Green’s function.References
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Additional Information
- Jeffrey Diller
- Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
- Email: diller.1@nd.edu
- Vincent Guedj
- Affiliation: Centre de Mathématique et Informatique, Université Aix-Marseille 1, Latp, 13453 Marseille Cedex 13, France
- Email: guedj@cmi.univ-mrs.fr
- Received by editor(s): November 10, 2006
- Received by editor(s) in revised form: August 28, 2007
- Published electronically: April 7, 2009
- Additional Notes: The first author gratefully acknowledges support from National Science Foundation grant DMS06-53678 during the preparation of this article.
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 4783-4805
- MSC (2000): Primary 32H50, 37F10, 37D25
- DOI: https://doi.org/10.1090/S0002-9947-09-04740-0
- MathSciNet review: 2506427